POM41210.1177/0305735612442582Ockelford and SergeantPsychology of Music 4425822012 Article Psychology of Music 41(2) 139 –174 Musical expectancy in atonal © The Author(s) 2012 Reprints and permission: sagepub. contexts: Musicians’ perception co.uk/journalsPermissions.nav DOI: 10.1177/0305735612442582 of “antistructure” pom.sagepub.com Adam Ockelford University of Roehampton, UK Desmond Sergeant Institute of Education, UK Abstract Two exploratory studies examine how 12-tone rows are processed cognitively. Tone-rows use each pitch-class once, and were devised by the composer Arnold Schoenberg as a way of structuring music in the absence of tonality, an approach subsequently known as “serialism”. One form of “antistructure” implied in the design of tone-rows – eschewal of pitch repetition – is explored using the “probe-tone” method, where subjects rate how well a pitch stimulus fits in a given context. The results support the finding of Krumhansl, Sandell and Sergeant that listeners can detect – and come to expect – the avoidance of pitch repetition. This cognitive strategy is modelled using Ockelford’s “zygonic” theory of music-structural understanding. A further study examines the second form “antistructure” implicit in serialist thinking (though not always adhered to in practice): the avoidance of patterns of intervals that give rise to a sense of key in suitably encultured listeners. Here, the discrepancies between the outputs of the zygonic model and the probe-tone ratings suggest that, despite the structural atonality, tonal schemata may also feature in the listening experience. These are evaluated using supplementary data gathered in a task where subjects were asked to identify potential “tonal flecks” in tone-row segments. Keywords cognition, expectation, probe-tone, serial music, structure, zygonic Introduction Zygonic theory and antistructure The notion of “antistructure” in music was posited by Adam Ockelford in the first main exposition of his “zygonic” theory (Ockelford, 1993). This asserts that musical structure stems Corresponding author: Adam Ockelford, Director, Applied Music Research Centre, Roehampton University, London SW15 5PU, UK. Email: [email protected] Downloaded from pom.sagepub.com at SAGE Publications on July 19, 2016 140 Psychology of Music 41(2) from a sense of derivation, whereby musical elements, whatever their perceptual domain, are (typically nonconsciously) heard as existing in imitation of another or others. The relationships – hypothesized cognitive constructs – through which such derivation is held to occur are said to be “zygonic” (from the Greek word for “yoke,” implying the union of two similar things). “Zygons” constitute a special type of “interperspective relationship,” through which perceived aspects or “perspects” of musical sounds are compared. The perspects pertaining to individual notes include pitch, scale-degree, onset, duration, loudness, and timbre. Intersperspective relationships can be represented parsimoniously in graphical form as shown in Figure 1.1 The proposition of “antistructure” is this: just as a given musical event has the quality of being what it is, since in perceptual terms the event comprises a set of features that can exist in a number of potential states, the event also has the quality of being what it is not. It is postulated that this quality of not being may also be imitated, thereby forming what may be termed “antistructure” (Ockelford, 1993, p. 101). This is not the absence of structure, but, rather, its obverse, or opposite. Examples from western classical music – in the domain of timbre – are to be found in those concerti where composers have consciously omitted the soloist’s sound from the main body of players. For instance, Richard Strauss’s Oboe Concerto (1945) uses a small orchestra of two flutes, cor anglais, two clarinets in B♭, two bassoons, two horns in F, violins, violas, ’celli and basses. In the context of the concerto, the tone colours of these instruments are united in sharing the quality not being an oboe. Hence they are linked antistructurally. This notion can be represented schematically as follows (see Figure 2; cf. Ockelford, 1993, p. 49). According to Ockelford’s (2005) analysis, an example of antistructure in the domain of pitch occurs in the first of Arnold Schoenberg’s Drei Klavierstücke, Op. 11. In the opening section (‘Mäßige’, bars 1–11), all pitch-classes are used except E♭. However, this value is particularly prominent in the first melodic gesture of the section that follows (“viel schneller,” bars 12ff.), forming the lowest note in the texture up to that point, and providing the springboard from which a new, rapidly ascending, arpeggiated figure is launched. Arguably, then, this first appearance of the E♭ pitch-class adds to the sense that “here is something different.” The ontological status of antistructure For music theorists, propositions such as these are, at least in principle, unproblematic. They would consider it reasonable to argue that the reading of the first Klavierstück shown in Figure 3 may act as an “ear-opener” (Dubiel, 1999, p. 274), pointing listeners towards an antistructural feature (that is, pitch-classes in the first section sharing the quality of not being E♭) that subsequently assumes structural significance in Section 2 (through an E♭ in the second octave being repeated in the bass). For music psychologists, however, concerned more with “typical” listeners (rather than individuals with a high degree of expertise or score-specific knowledge – see, for example, Margulis, 2005, pp. 334 and 335), the value of observations like these is less clear. For them, the significant issue is likely to be whether the identified “antistructure” has any perceptual (albeit nonconscious) reality. The challenges of testing conjectures of this kind empirically lie at the heart of this article, and are considered in some detail below. There is a third perspective that musicologists may wish to take into account: that of the composer. What were Schoenberg’s intentions in relation to this aspect the piece? While there is no documentary evidence that he fashioned Op. 11, No. 1 with the initial omission of the E♭ in mind, it may have been a feature of his thinking, though the antistructural procedure Downloaded from pom.sagepub.com at SAGE Publications on July 19, 2016 Ockelford and Sergeant 141 “Primary zygonic relationship of duration”: indicates that the length “Primary interperspective of the second note “Secondary zygonic relationship of scale degree”: is deemed to exist in relationship of Scale degree”: gauges the (melodic) imitation of the first indicates that the second melodic interval between two notes interval (gauged in terms in terms of degrees of the of difference of scale degree) is pertinent scalar framework deemed to exist in imitation of the first “Primary zygonic relationship of pitch”: indicates that the pitch of the second note is deemed to exist in imitation of the first Moderato cantabile molto espressivo “Primary interperspective relationship”: gauges the difference between the onsets of two notes “Secondary interperspective relationship”: gauges the difference between Beethoven: two primary relationships of onset Piano Sonata, Op. 110; “Tertiary zygonic relationship”: first Movement indicates that (in the ear of the analyst) the later secondary relationship of onset exists in imitation of the earlier one Figure 1. Examples of interperspective and zygonic relationships Downloaded from pom.sagepub.com at SAGE Publications on July 19, 2016 142 Psychology of Music 41(2) clarinet bassoon non-zygonic cor anglais relationships T 1 horn T T 1 1 T 1 Timbre oboe ute T 1 1 T T violin 1 1 T 1 bass viola cello set of antizygonic relationships linking ”not oboe” the orchestral timbres T 1 Figure 2. Example of antistructure in the domain of timbre in Strauss’s Oboe Concerto identified here arguably foreshadows the principle of avoiding of pitch-class recurrence that characterized the composer’s subsequent “serial” writing (Schoenberg, 1948/1975, p. 247). In summary, then, though the ontological status of the antistructure we identify in the first Klavierstück is unclear (see Figure 4), it is also non-contentious: Ockelford’s (2005) analysis highlights a feature that makes no general claim to be part of listeners’ conceptual awareness (though it could conceivably exert a subliminal effect). Serialism, atonality2 and antistructure – the perspectives of composers, theorists and music psychologists However, there are other instances of antistructure whose ontological status is a matter of some debate; for example, the property of tone-rows that no pitch-class may be repeated until all 12 have been presented, as described above. Schoenberg’s position is this (1948/1975, p. 246): Downloaded from pom.sagepub.com at SAGE Publications on July 19, 2016 Ockelford and Sergeant 143 Schoenberg, Op. 11, No. 1 Mäßige ' %% !( " # " " " " " & " & " " ' " " % ( # rit. langsamer " # " " ! "# % #&# " $ $ " $ % " $ & " $ # % # 12 viel schneller $ ! " # " & set of pcs used, bars 1–11 Enot Pc "& & 1 universal set of pcs Figure 3. Antistructure purported to operate in the domain of pitch in Schoenberg’s first Klavierstück, Op. 11 Figure 9.13 Antistructure postulated to operate in the domain of pitch The construction of a basic inset Schoenberg’s of twelve tones first derives Klavierstück from the intention, Op. 11 to postpone the repetition of every tone as long as possible … [since] the emphasis given